Today, the publication of microdata poses a privacy threat: anonymous personal records can be re-identified using third data sources. Past research has tried to develop a concept of privacy guarantee that an anonymized data set should satisfy before publication, culminating in the notion of t-closeness. To satisfy t-closeness, the records in a data set need to be grouped into Equivalence Classes (ECs), such that each EC contains records of indistinguishable quasi-identifier values, and its local distribution of sensitive attribute (SA) values conforms to the global table distribution of SA values. However, despite this progress, previous research has not offered an anonymization algorithm tailored for t-closeness. In this paper, we cover this gap with SABRE, a SA Bucketization and REdistribution framework for t-closeness. SABRE first greedily partitions a table into buckets of similar SA values and then redistributes the tuples of each bucket into dynamically determined ECs. This approach is facilitated by a property of the Earth Mover’s Distance (EMD) that we employ as a measure of distribution closeness: If the tuples in an EC are picked proportionally to the sizes of the buckets they hail from, then the EMD of that EC is tightly upper-bounded using localized upper bounds derived for each bucket. We prove that if the t-closeness constraint is properly obeyed during partitioning, then it is obeyed by the derived ECs too. We develop two instantiations of SABRE and extend it to a streaming environment. Our extensive experimental evaluation demonstrates that SABRE achieves information quality superior to schemes that merely applied algorithms tailored for other models to t-closeness, and can be much faster as well.